Question

To find the maximum value of the function xyz by Lagrange method of
multipliers under the constraints x2 + z2 1 and y-x=0, how many
Lagrange multipliers are required
(a) 1
(b) 2
(c)3
(d) 4

Answer 1

Solve the following system of equations. ∇f(x,y,z)=λ∇g(x,y,z)g(x,y,z)=k.

Plug in all solutions, (x,y,z) ( x , y , z ) , from the first step into f(x,y,z) f ( x , y , z ) and identify the minimum and maximum values, provided they exist and ∇g≠→0 ∇ g ≠ 0 → at the point.